[Edu-sig] generate digits of pi

[david at handysoftware.com]

Here's an easier, pythonic way to limit the number of digits, given the original, non-terminating pi generator:
 
>>> import itertools
>>> print(list( itertools.islice(pi_digits(), 10) ))
[3, 1, 4, 1, 5, 9, 2, 6, 5, 3]
 
David H
 
-----Original Message-----
From: "michel paul" <pythonic.math at gmail.com>
Sent: Sunday, December 23, 2012 6:49pm
To: "Kirby Urner" <kurner at oreillyschool.com>
Cc: david at handysoftware.com, "edu-sig at python.org" <edu-sig at python.org>, "michel paul" <pythonic.math at gmail.com>
Subject: Re: [Edu-sig] generate digits of pi



I realized something. This was the original version:




def pi_digits():


k, a, b, a1, b1 = 2, 4, 1, 12, 4


while True:


p, q, k = k*k, 2*k+1, k+1


a, b, a1, b1 = a1, b1, p*a+q*a1, p*b+q*b1


d, d1 = a/b, a1/b1


while d == d1:


yield int(d)


a, a1 = 10*(a%b), 10*(a1%b1)


d, d1 = a/b, a1/b1

I forget where it came from. Like I had mentioned, I had a really bright student awhile back who was really intrigued by this, and he at one point edited it to produce the digits in binary. In the original form the generator never terminates. Somewhere along the line an edit was made to try to get it to terminate at n digits. Probably to make calling it easy to call as in list(pi_digits(n)).
- Michel



On Sat, Dec 22, 2012 at 5:34 PM, Kirby Urner <[mailto:kurner at oreillyschool.com] kurner at oreillyschool.com> wrote:
Got it, no wrong digits just not always exactly the number you asked for.

This happens often in 3.2 as well:

>>> exp = ((n,len(list(pi_digits(n)))) for n in range(10000))  # (number asked, number got)
 >>> exp2 = ((a,b) for a,b in exp if a != b)  # filter on "not same"
>>> for i in range(10): print(next(exp2), end=", ") 
(2, 3), (4, 5), (10, 11), (16, 17), (18, 19), (22, 23), (28, 31), (29, 31), (30, 31), (34, 36),

Kirby





On Sat, Dec 22, 2012 at 4:40 PM,  <[mailto:david at handysoftware.com] david at handysoftware.com> wrote:

In each case I asked for only 79 digits, but got 79, 82, and 83 digits depending on whether I was using python 3.2, python 2.6, or python 2.6 with -Qnew, respectively. The digits all seem to be correct, but the algorithm for stopping at digit n seems to be very sensitive.
 
David H
 
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